Summary
The effect of the combination of breeding and migration on linkage in a subdivided population can be treated by means of a direct product structure. The eigenvalues of the combined operator are investigated and the theory placed in a general setting.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abraham, V. M.: Linearising quadratic transformations in genetic algebras. Unpublished Ph. D. thesis. Univ. of London (1976).
Bennett, J. H.: On the theory of random mating. Ann. Eugen. 18, 311–317 (1954).
Etherington, I. M. H.: Duplication of linear algebras. Proc. Edinburgh Math. Soc. (2) 6, 222–230 (1941).
Ewens, W. J.: Population Genetics. London: Methuen 1969.
Feldman, M. W., Christiansen, F. B.: The effect of population subdivision on two loci without selection. Genet. Res. 24, 151–162 (1975).
Holgate, P.: Sequences of powers in genetic algebras. J. London Math. Soc. 42, 489–496 (1967).
Holgate, P.: Interaction between migration and breeding studied by means of genetic algebras. J. Appl. Prob. 5, 1–8 (1968).
Holgate, P.: The genetic algebra of k linked loci. Proc. London Math. Soc. (3) 18, 315–327 (1968).
Holgate, P.: Characterisations of genetic algebras. J. London Math. Soc. (2) 6, 169–174 (1971).
Nei, M., Li, W. H.: Linkage disequilibrium in subdivided populations. Genetics 75, 213–219 (1973).
Schafer, R. D.: Structure of genetic algebras. American J. Math. 71, 121–135 (1949).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Holgate, P. Direct products of genetic algebras and Markov chains. J. Math. Biol. 3, 289–295 (1976). https://doi.org/10.1007/BF00275061
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00275061